20ed5/3

This page is a stub. You can help the Xenharmonic Wiki by expanding it.

← 19ed5/3

20ed5/3

21ed5/3 →

Prime factorization	22 × 5
Step size	44.2179¢
Octave	27\20ed5/3 (1193.88¢)
Twelfth	43\20ed5/3 (1901.37¢) (convergent)
Consistency limit	10
Distinct consistency limit	4

20 equal divisions of 5/3 (abbreviated 20ed5/3) is a nonoctave tuning system that divides the interval of 5/3 into 20 equal parts of about 44.2 ¢ each. Each step represents a frequency ratio of (5/3)^1/20, or the 20th root of 5/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	44.218
2	88.436	18/17, 19/18, 20/19, 21/20, 22/21, 23/22
3	132.654	13/12, 14/13, 15/14, 25/23
4	176.872	10/9, 11/10, 19/17, 21/19
5	221.09	8/7, 17/15, 25/22
6	265.308	7/6, 22/19
7	309.526	6/5, 19/16, 25/21
8	353.743	11/9, 16/13, 21/17
9	397.961	5/4, 19/15, 24/19
10	442.179	9/7, 13/10, 22/17
11	486.397	4/3, 21/16, 25/19
12	530.615	15/11, 19/14, 23/17
13	574.833	7/5, 18/13, 25/18
14	619.051	10/7
15	663.269	19/13, 22/15, 25/17
16	707.487	3/2
17	751.705	14/9, 17/11, 20/13, 23/15
18	795.923	11/7, 19/12
19	840.141	13/8, 18/11, 21/13
20	884.359	5/3

Harmonics

Approximation of harmonics in 20ed5/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-6.1	-0.6	-12.2	-0.6	-6.7	-8.3	-18.3	-1.2	-6.7	+5.2	-12.8
	Relative (%)	-13.8	-1.3	-27.7	-1.3	-15.2	-18.7	-41.5	-2.6	-15.2	+11.7	-29.0
Steps (reduced)		27 (7)	43 (3)	54 (14)	63 (3)	70 (10)	76 (16)	81 (1)	86 (6)	90 (10)	94 (14)	97 (17)

Approximation of harmonics in 20ed5/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-18.7	-14.4	-1.2	+19.8	+3.2	-7.3	-12.5	-12.8	-8.8	-0.9	+10.5
	Relative (%)	-42.4	-32.5	-2.6	+44.7	+7.3	-16.5	-28.2	-29.0	-20.0	-2.1	+23.8
Steps (reduced)		100 (0)	103 (3)	106 (6)	109 (9)	111 (11)	113 (13)	115 (15)	117 (17)	119 (19)	121 (1)	123 (3)